Influence of the System Geometry on the Characteristics of the Surface Tension Auto-oscillations:  A Numerical Study

Abstract

A numerical study of the processes that occur in a small cylindrical vessel with rigid walls, by the dissolution of a surfactant droplet placed on the capillary tip under the free water interface, is presented. Periodically arising Marangoni instability reveals itself in auto-oscillations of the surface tension. The effect of geometrical factorssnamely, capillary immersion depth, capillary and droplet radii, and container height and radiusson the auto-oscillation characteristics is analyzed. The numerical and experimental results are compared and discussed.

Periodic Elastic Motion in a Self-Assembled Monolayer under Spontaneous Oscillations of Surface Tension: Molecules in a Scrum Push Back a Marangoni Flow

“…Previously predicted by numerical simulations, the oscillatory regime without a spread monolayer on the water surface should occur either by an increase in the capillary immersion depth or by a decrease in the size of the liquid container. 20 In the study presented here with a spread monolayer, the oscillatory regime was strongly related to the surface pressure of the monolayer. The Marangoni convective flow near the capillary was investigated to elucidate the oscillation mechanism.…”

“…15−19 Regular oscillations have been observed for a couple of days in a certain range of liquid container diameters to the immersion depth of the surfactant droplet in the water. 20 These phenomena have been understood macroscopically using fluid mechanics. Most of the previous work has focused on the flow dynamics emerging from the diffusion of a surfactant from a droplet to understand the spontaneous oscillations of surface tension.…”

“…The Marangoni effect is the convective mass transfer along an interface between two fluids due to a gradient of surface tension. − When a surfactant droplet is placed on a water surface, the droplet can start running over the surface − and spreads until a uniform monolayer is formed on the water surface. When a surfactant droplet is suspended under the water surface, the surfactant molecules that diffuse to the water surface also induce a Marangoni flow, which can lead to spontaneous oscillations of the surface tension under the right conditions. − Regular oscillations have been observed for a couple of days in a certain range of liquid container diameters to the immersion depth of the surfactant droplet in the water . These phenomena have been understood macroscopically using fluid mechanics.…”

Surfactant Transfer through a Liquid Membrane: Origin of Spontaneous Oscillations at the Membrane/Acceptor Phase Interface

“…To validate this assumption we performed a theoretical analysis of a simplest liquid membrane system, and it was possible to show that this system produces spontaneous nonlinear oscillations. For the theoretical analysis we used the approach successfully applied earlier for the oscillations produced by surfactant transfer from a point source. − This approach consists of a direct numerical simulation of the system behavior on the basis of the first principles. Then we studied a similar system experimentally and confirmed the theoretical conclusions.…”

Nonlinear Spontaneous Oscillations at the Liquid/Liquid Interface Produced by Surfactant Dissolution in the Bulk Phase

“…However, the correlations between the physicochemical and hydrodynamic processes and, therefore, the actual mechanisms underlying the behavior of these systems are not quite clear to date. System 3 is the simplest among the four considered systems, and the oscillation mechanism as well as the effect of the various system characteristics have been established for system 3 employing direct numerical simulation of the system evolution. − According to the developed theory, auto-oscillation of the surface tension is the result of Marangoni instability periodically arising and fading. The instability fades due to the interaction of the longitudinal wave, generated by instability, with the vessel wall.…”